16 STRENGTH OF MATERIALS 



may be permanently deformed by stresses below the elastic limit. 

 The reason for this is that the smallest dimension of such a bod 

 is of the same order of magnitude as the deformation of one of the 

 other dimensions, and consequently Hooke's law does not apply in 



this case. 



21. Factor of safety. In order to assure absolute stability to any 

 structure it is clear from what precedes that the actual stresses 

 occurring in the structure must not exceed the elastic limit of the 

 material used. 



For many materials, however, it is very difficult to determine tin- 

 elastic limit, while for other materials for which the determin;. 

 is easier, such as iron and steel, the elastic limit is subject to large 

 variations in value, and it is impossible to do more than a.- 

 limits within which it may be expected to lie. For this reason it i 

 customary to judge the quality of a material by its ultimate 

 instead of by its elastic limit, and assume a certain fraction of the 

 ultimate strength as the allowable working stress. 



The number which expresses the ratio of the ultimate stn 

 the working stress is called the factor of safety. Thus 



Factor of safety = 



workl , l(f str , ss 



No general and rational method of determining the factor of sa; 

 can be given. For, in the first place, formulas deduced from tin- 

 ical considerations rest on the assumption that the m. 

 is perfectly elastic, homogeneous, and isotropie, an as>umpii.n which 

 is never completely fulfilled. Such formulas give, therefore, only an 

 approximate idea of the state of stress within the body. 



Moreover, the forms of construction members assumed for pur- 

 poses of calculation do not exactly correspond to those actually n 

 also certain conditions are unforeseen, and therefore uMpruviile.: 

 such as the sinking of foundations, accidental shocks, etc. 



In metal constructions rust is another element which ten<U t, 

 reduce their strength, and in timber constructions the same is 

 true of wet and dry rot. Care is usually taken toj.iwent ru>t ami 

 decay, but the preservative processes used never perfectly accomplish 

 their object. 



